On shared hosting, you're lucky to have quiz work even for a few users. Shared hosting (as name suggests) are with shared resources, on a typical shared host you get 25% of 1 CPU core and 1GB of SHARED memory allocated to one account. If it wouldn't have been blessings of SSD Drives and improved Instructions per clock of newer CPUs', you would hardly be able to even install moodle on shared server, so consider shared server for your moodle testing or a very new moodle installation where you are starting to collect users and not a fully operational moodle with quizzes.
as you asked, to prevent this issue - either get only 10 users at a time to take quiz, or think of upgrading to a VDS or Dedicated (not even VPS)
as you asked, to prevent this issue - either get only 10 users at a time to take quiz, or think of upgrading to a VDS or Dedicated (not even VPS)